English

Esakia order-compactifications and locally Esakia spaces

Logic 2025-12-29 v1 General Topology

Abstract

We introduce Esakia order-compactifications and study how they fit in the general theory of Priestley order-compactifications. We provide an analog of Dwinger's theorem by characterizing Esakia order-compactifications by means of special rings of upsets. These considerations naturally lead to the notion of a locally Esakia space, for which we prove that taking the largest Esakia order-compacification is functorial, thus obtaining an analog of Banaschewski's theorem.

Cite

@article{arxiv.2512.22042,
  title  = {Esakia order-compactifications and locally Esakia spaces},
  author = {Rodrigo Nicolau Almeida and Guram Bezhanishvili and Nick Bezhanishvili},
  journal= {arXiv preprint arXiv:2512.22042},
  year   = {2025}
}

Comments

19 pages, 3 figures

R2 v1 2026-07-01T08:41:36.454Z